Fellow's insurance not complete (4)
I believe the answer is:
cove
'fellow's' is the definition.
(British slang term)
'insurance not complete' is the wordplay.
'insurance' becomes 'cover' (I've seen this before).
'not complete' means to remove the last letter.
'cover' with its final letter removed is 'COVE'.
(Other definitions for cove that I've seen before include "Bloke; bay" , "A small inlet or estuary" , "Rum fellow found in a small inlet" , "Small bay or Dickensian chap" , "where the sea comes in" .)